Indistinguishability of causal relations from limited marginals

Abstract

We investigate the possibility of distinguishing among different causal relations starting from a limited set of marginals. Our main tool is the notion of adhesivity, that is, the extension of probability or entropies defined only on subsets of variables, which provides additional independence constraints among them. Our results provide a criterion for recognizing which causal structures are indistinguishable when only limited marginal information is accessible. Furthermore, the existence of such extensions greatly simplifies the characterization of a marginal scenario, a result that facilitates the derivation of Bell inequalities both in the probabilistic and entropic frameworks, and the identification of marginal scenarios where classical, quantum, and postquantum probabilities coincide.

arXiv comment16 pages, 9 figures

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Cited by in corpus (12)

• Kochen-Specker Contextuality
• The Inflation Technique for Causal Inference with Latent Variables
• Necessary and sufficient condition for contextuality from incompatibility
• Analysing causal structures with entropy
• The entropic approach to causal correlations
• A convergent inflation hierarchy for quantum causal structures
• Restrictions for the Causal Inferences in an Interferometric System
• On Possibilistic Conditions to Contextuality and Nonlocality
• Computational tools for solving a marginal problem with applications in Bell non-locality and causal modeling
• Monogamy of Temporal Correlations: Witnessing non-Markovianity Beyond Data Processing
• Quantum Causal Structure and Quantum Thermodynamics
• Differential Geometry of Contextuality